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The pandemic linked to COVID-19 infection represents an unprecedentedclinical and healthcare challenge for many medical researchers attempting toprevent its worldwide spread. This pandemic also represents a major challengefor statisticians involved in quantifying the phenomenon and in offering timelytools for the monitoring and surveillance of critical pandemic parameters. In arecent paper, Alleva et al. (2020) proposed a two-stage sample design to builda continuous-time surveillance system designed to correctly quantify the numberof infected people through an indirect sampling mechanism that could berepeated in several waves over time to capture different target variables inthe different stages of epidemic development. The proposed method exploits theindirect sampling (Lavalle, 2007; Kiesl, 2016) method employed in theestimation of rare and elusive populations (Borchers, 2009; Lavall\'ee andRivest, 2012) and a capture/recapture mechanism (Sudman, 1988; Thompson andSeber, 1996). In this paper, we extend the proposal of Alleva et al. (2020) toinclude a spatial sampling mechanism (M\"uller, 1998; Grafstr\"om et al., 2012,Jauslin and Till\`e, 2020) in the process of data collection to achieve thesame level of precision with fewer sample units, thereby facilitating theprocess of data collection in a situation where timeliness and costs arecrucial elements. We present the basic idea of the new sample design,analytically prove the theoretical properties of the associated estimators andshow the relative advantages through a systematic simulation study where allthe typical elements of an epidemic are accounted for.

Spatial sampling design to improve the efficiency of the estimation of the critical parameters of the SARS-CoV-2 epidemic